The extended Schwarz's lemma, the maximum modulus theorem, and the structure of the zero sets defined in the newly constructed theory of regular functions and polynomials of a quaternionic variable are used to deduce the bounds for the zeros of these polynomials and regular functions. Our ...
16.The closer ε to zero, the avalanche size distribution is more approximate to power function, exhibiting quasi-SOC property.随着ε趋于0,崩塌规模分布越来越接近于幂函数,表现出准自组织临界的特性。 17.General Form of Bounded Linear Functionals on K the Function Space;K the函数空间上有界线性泛函...
In the following theorem, [Math Processing Error]Z denotes the zero section of the bundle [Math Processing Error]T∗M×2. Theorem 2.1 Let [Math Processing Error]u1,u2 be distributions on [Math Processing Error]M×2 of positive type such that for all [Math Processing Error](x,ξ)∈T...
than any of the others, then it is the upper bound ofE. If, however, there is no such greatest number among the numbers ofE, this set may still have an upper bound. For example, the upper bound of all negative numbers is equal to zero. The set of all positive numbers is not ...
作者: C Liu 摘要: It is proven that there are innitely many pairs of distinct primes whose dierence is no greater than 84. The novelty is the construction of the largest sieve support which permits the use of the Bombieri-Vinogradov theorem. 年份: 2022 收藏...
It is evident from the above definitions that Ds(ρAB) ≤ Cr(ρAB)13, as this measure of discord is the minimum amount of the coherence in any product basis2. Results Linking quantum coherence to quantum discord Theorem 1 For any bipartite state ρAB, it holds \({D}_{A| B}^{...
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The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen et al. (Numer Math 149(2):273–304, 2021) require a parameterthat is foundnotrobust as the polynomial degreepincreases. This is related to thestability bound of theprojection onto polynomials...
Our main technique is Talagrand's (1995) isoperimetric theorem. Our result shows a better behavior of the wavelet shrinkage.关键词: wavelet transforms signal reconstruction signal sampling mean square error methods deviation bounds wavelet shrinkage signal reconstruction noisy samples deviation estimate ...
The aim is to predict what would be the highest allowable stress amplitude that the composite can endure ('the endurance limit') when undergoing 'infinite' number of cyclic loading. To reach this goal we employ (a) Melan's static shakedown theorem for formulating the lower bound to the ...